Question

The weight of coffee (in $gms$) in $70$ packets is given in the following table.

Weight (in $gms$)	No. of Packets
$200-201$	$12$
$201-202$	$26$
$202-203$	$20$
$203-204$	$9$
$204-205$	$2$
$205-206$	$1$

Hence determine the modal weight of coffee packet.

Answer 1

Weight(in $gms$)	No. of Packets
$200-201$	$12$
$201-202$	$26$
$202-203$	$20$
$203-204$	$9$
$204-205$	$2$
$205-206$	$1$

Here the maximum frequency $f_m=26$

The corresponding class $201-202$ is the modal class.

$L=201,f_m=26,f_1=12,f_2=20,h=1$

Mode $=L+(\frac{f_m-f_1}{2f_m-f_1-f_2})h$

$=201+(\frac{26-12}{2\times 26-12-20})1$

$=201+(\frac{14}{20})$

$=201+\frac{7}{10}$

$=201.7$

Modal weight of the coffee is $201.7gms.$